(1) The unit vector in the direction of the vector 37+ 4k is (2) The dot product (-2,1,3) (5,4, 3) = (3) The domain of f(x,y) = In(x2 + y? – 1) is (4) Suppose f(x, y) = xe*+y. Then f,(1,-1) = %3D 6 (5) The double integral S, 3x²ydxdy =

Q: 13. Find a vector equation of the line through (2, 1) parallel to (x, y) = (-2,7)+t(3,5). 14. Find a…

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Q: Do only question 6

A: Evaluate fx​(3,1)Evaluate fy​(3,1)Find the derivative of f(x,y) with respect to x, treating y as a…

Q: Let x(¹) (t) = = -3t e 4e-3t, 0 0 x (²) (t) = [_5e-31]. -5e-3t, 0 Are the vectors x(¹) (t), x(²) (t)…

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Q: Do question two only

A: Step 1: Assign variablesFrom the givena=⟨4,6,9⟩b=⟨−6,−3,2⟩Let:xa = 4ya = 6za = 9xb = -6yb = -3zb = 2…

Q: Use the function to find the image of v and the preimage of w. T(v1, v2, v3) = (4v2 - v1, 4v1 +…

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Q: Do question 12 only

A: The given in item #12 is:∫04π​​∫01​∫0x2​xcos(y) dz dx dy Consider the innermost…

Q: Do only question 5

A: Step 1:Identify the variable you're differentiating with respect to. Let's say you want to find…

Q: Express the vector v = -12 -28 as a linear combination of x = 2 [² and y= -1 -6

A: We can write the answer in the below steps.

Q: Find a vector equation for the line through the point (4, 5, -1) perpendicular to the vectors , 6,…

A: we have to find the line equation passing through point (4,5,-1) and perpendicular to the vectors…

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: Do question 10 only

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Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4V1 +…

A: Given  T(v1,v2,v3) = (4v2-v1,4v1+5v2)Image of v is given by T(1,-2,-4) = (-9,-6) hence (a). the…

Q: Find the vector in component form with initial poi

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Q: (2) Determine if the vectors are linear independent or linear dependent. Justify your answer. (a)…

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Q: Do only question 8

A: To find the equation of the plane tangent to the surface  f(x,y)=x+yx​ at the point (1, 2), we need…

Q: Do only question 4

A: Questio(4)Part(a)Find limt→∞​r(t):Given r(t)=⟨2sin(t),3cos(t),t2⟩, as t→∞,sin(t) and cos(t)…

Q: Use the function to find the image of v and the preimage of w. T(V1, V2, V3) = (4v2 – V1, 4v, +…

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Q: Do question 9 only

A: Step 1: Compute the Gradient of 𝑓Given f(x,y)=x2ey,Compute the partial…

Q: Use the function to find the image of v and the preimage of w. T(V₁, V2, V3) = (4V2 V₁, 4v₁ + 5v₂),…

A:

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.